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Small generators of function fields

Martin Widmer (2010)

Journal de Théorie des Nombres de Bordeaux

Let 𝕂 / k be a finite extension of a global field. Such an extension can be generated over k by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.

Solving conics over function fields

Mark van Hoeij, John Cremona (2006)

Journal de Théorie des Nombres de Bordeaux

Let F be a field whose characteristic is not  2 and K = F ( t ) . We give a simple algorithm to find, given a , b , c K * , a nontrivial solution in  K (if it exists) to the equation a X 2 + b Y 2 + c Z 2 = 0 . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in F ; hence we obtain a recursive algorithm for solving diagonal conics over ( t 1 , , t n ) (using existing algorithms for such equations over  ) and over 𝔽 q ( t 1 , , t n ) .

Sur la transcendance de la série formelle Π

Jean-Paul Allouche (1990)

Journal de théorie des nombres de Bordeaux

En utilisant le théorème de Christol, Kamae, Mendès France et Rauzy, nous donnons une démonstration élémentaire de la transcendance de la série formelle Π ainsi que d’autres séries formelles à coefficients dans un corps fini.

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